This week's
colloquium takes a look at an old "proof" for the four color theorem

Title: Alfred
Kempe's "Proof" of the Four Color Theorem

Speakers: Tim Sipka, Alma
College

Time: Thursday,
October 20 at 11:00 am

Place: VWF 102

Abstract: The four color
theorem is a simple and believable statement: at most four colors are needed
to color any map drawn in the plane or on a sphere so that no two regions
sharing a boundary receive the same color. It might be surprising
to find out that mathematicians searched for a proof of this statement for
over a century until finally finding one in 1976. In this talk we'll
consider the "proof" given by Alfred Kempe that was published in 1879 and
thought to be correct until a flaw was found in 1890. You'll be
invited to look carefully at Kempe's proof and see if you can do what many
19th century mathematicians could not do---find the flaw.

Note: We
have a nontypical day, time, and location for this week's colloquium.

Next week's
colloquium

Title: Lights
Out: Some Puzzles, Some Results, and Some Questions

Speakers: Darin Stephenson,
Hope College

Time: Tuesday,
October 25 at 4:00 pm

Place: VWF 104

Abstract: In the
“Lights Out” puzzle, the solver seeks to turn off all
of a set of lights (often represented by the vertices on a graph) by pressing
a series of buttons, each of which has a certain predefined effect on the
lights. The lights each have an “initial state” (typically “on” or
“off”), and an initial configuration of states is called solvable if there
is a process for turning off all of the lights. The solution to any
specific version of this puzzle can be phrased in terms of matrix algebra.
Our overall goal is to study this problem in generality, and, eventually,
to characterize the solvable initial configurations for certain families
of graphs. In this talk, we will provide a survey of the classical
Lights Out puzzle, discuss many generalizations and some known results, and
give a few questions that may serve as motivation for collaborative faculty-student
research in summer 2012.

Note: Please come
to enjoy refreshments with the speaker, the faculty, and fellow mathematics
students before the colloquium at 3:30 pm in VanderWerf 222.

Help out MDY's
Mathemagicians in the upcoming Relay for Life

In the wake of Mary DeYoung’s death after a brief
battle with cancer this past summer, many students are looking for ways
to honor and celebrate her life. One of these opportunities presents itself
in this year’s Relay for Life at Hope College. A team has been formed for
all of us to remember Mary DeYoung and to help raise money to fight this
horrible disease. You can support the team in any of the following four ways:

Join the team, raise funds, and walk with us at Relay
for Life on November 11-12 from 7pm to 7am. If you want to join just go
to http://relayforlifehope.com,
click SIGN UP, and then JOIN A TEAM. Look for MDY's Mathemagicians.

Make a donation to team. Either online or by getting the
money to one of the team captains: Rachel Elzinga, Morgan Bell, and Nicholle
Taurins. There will also be a collection can in the math department office.

Decorate a luminaria in honor of Mary DeYoung or anyone
else you know who has been touched by cancer. Luminarias are bags lit
by electric lights to honor survivors and people who have lost their battle
with cancer. They will line the track during the Relay event and will
be honored during a ceremony. Usually people donate $5-$10 for a luminary,
but anyone who is interested can make one regardless of whether or not they
donate. Simply contact Rachel, Morgan, or Nicholle and we will get you a
bag.

Pray for the team as we work to raise money for the American
Cancer Society to honor Mary DeYoung.

Even if you can’t join, check out the team page by going to http://relayforlifehope.com,
look for “Top Teams” on the right hand side, click “View All”, and then
click “MDY’s Mathemagicians” to see updates on fundraising and team activities.
If you have any questions or ideas please contact Rachel Elzinga
(rachel.elzinga@hope.edu), Morgan Bell (morgan.bell@hope.edu) or Nicholle
Taurins (nicholle.taurins@gmail.com).

Thanks for helping us work towards a world with less cancer and more
birthdays!

MATH Challenge

The 2011 Michigan
Autumn Take Home Challenge (or MATH Challenge) will take place on the
morning (9:30am - 12:30pm) of Saturday, November 5 this year. Teams
of two or three students take a three-hour exam consisting of ten interesting
problems dealing with topics and concepts found in the undergraduate mathematics
curriculum. Each team takes the exam at their home campus under the
supervision of a faculty advisor.

The department pays the registration fee for each team and will provide
lunch to participants afterwards. The sign-up deadline is Monday, October 24 at 4:00 p.m. Interested
students can sign up by sending Prof. Yurk an email at yurk@hope.edu or
by signing up on the list on his door (VWF 214).

A group of students may sign up as a team. Individual students
are also encourage to sign up; they will be assigned to a team.
For more information, please talk with any member of the Mathematics Department
or visit this link where you can also view old copies
of the exam.

Math in the News:
Scientists use Twitter to analyze public heath trends

Who would ever think that "omg i think
i have the flu going home bfn" would be of value to science. Well
according to a recent report from Discoveries
and Breakthroughs Inside Science, computer scientists at John Hopkins
University are using the online social networking and microblogging service
to track public health trends.

"There’s a lot of different patterns we were able to uncover,” said Mark
Dredze (Johns Hopkins), “so for example we were able to track the influenza
rate in the United States over time just by counting how many times people
are talking about the flu.”

Problem Solvers
of the Fortnight

In our last problem of the fortnight
we saw that Sally began
to solve a problem at the time between 4:00 and 5:00 p.m. when the clock's
hands are together. She finished when the minute hand is opposite
the hour hand. How many minutes does it take her to solve the problem,
and when does she finish it? Give exact answers in terms of fractions
of minutes (i.e. no decimal approximations).
Congratulations to Lauren Aprill, Ryan Martinez, Lute Olsen, Jessica
Hulteen, Jake Blysma, Craig Toren, Krisen Slotman, Corinna Schmidt, Danielle
Maly, Erice Budge, Emily Scott, Allison Leigon, Anna Filcik, Lisa McLellan,
Kristen Bosch, Bryce Ciroshek, Pete Stuckey, Hunter Ford, Brant Bechtel,
Sarah Prill, David Dolphin, Andrew Borror, Morgan Smith, Daniel Langholz,
Shinnosuke Kondo, Scott DeClaire, Melanie Leonard, Justin Kammeraad, Allie
Benson, Josh Swelt, Kevin Olson, Andrew Brooks, Nicole Zeinstra, Tim Lewis,
Tim Cooke, Matt Folkert -- all of whom correctly determined the exact starting
and ending time of the exam in the last Problem of the Fortnight.

Problem of the
Fortnight

You have ten stacks of coins, each consisting
of 10 new dollar coins. One entire stack of coins is counterfeit, but
you do not know which one. However, you do know the weight of a genuine
dollar coin, and you are also told that each counterfeit coin weighs one
gram more than it should. Your kind chemistry professor agrees to let
you weigh the coins on one of the electronic scale in the chem lab.

What is the smallest number of weighings necessary to determine which stack
is counterfeit, and how do you do it?

Attach a counterfeit dollar coin to your solution, and drop it in the Problem
of the Fortnight slot outside Professor Pearson's office (VWF 212) by 3:00
p.m. on Friday, October 28. As always, be sure to include your
name as well as the name(s) of your professor(s) -- e.g. Bo Guscoins, Professor
Cown TerFit -- on your solution.

The best
and most beautiful things in the world cannot be seen or even touched –
they must be felt with the heart.